Roberto Firmino has now scored 10 or more goals in all four of his Premier League seasons with Liverpool
Liverpool maintained the pressure on Premier League leaders Manchester City by coming from behind to beat Burnley in tricky conditions at Anfield.
The Clarets took a shock sixth-minute lead when Ashley Westwood scored direct from a corner, although it appeared Reds' goalkeeper Alisson had been impeded by James Tarkowski.
But the hosts were only behind for 13 minutes before Roberto Firmino tapped in after Tom Heaton had fumbled Mohamed Salah's cross.
In a first half played in strong wind and hailstorms, Liverpool took the lead when Sadio Mane curled a shot past Heaton.
Firmino scored his second following Heaton's poor clearance and Burnley pulled one back late on through Johann Berg Gudmundsson from six yards out.
But there was no fightback as Mane then went around the Clarets' keeper in injury time for his second and Liverpool's fourth to seal the win, which leaves Jurgen Klopp's side one point behind City with eight league games of the season remaining.
Liverpool fight hard for the three points
Liverpool, aiming to become English champions for the first time since 1990, had faced questions over their character after a run of four draws in six league matches had seen them lose their lead at the top of the table.
Raheem Sterling's hat-trick for Manchester City on Saturday gave Pep Guardiola's side a 3-1 win over Watford and left the defending champions with a four-point advantage.
Guardiola said it would be "almost impossible" to win every remaining league match and all Liverpool can do is win their own games and hope for a slip-up from City.
The hosts made the worst possible start, trailing early on, but Klopp's team responded in fine fashion and showed their character to dig deep and overcome a hard-working and determined Burnley outfit.
Firmino's shot was deflected over after 13 minutes, but six minutes later he had his 10th league goal of the season, scoring from close range after a mistake from Heaton following fine play from Salah, who had played a one-two with Georginio Wijnaldum.
The inclusion of Adam Lallana, making only his fifth start of the season, was met with doubt by many on social media - but he played a huge part in Liverpool's second, sliding in to block a clearance, with Ben Mee's subsequent challenge falling to Mane to curl past Heaton.
A second error from Heaton, who gifted the ball to Salah, led to the Reds' third, with Firmino finishing after Charlie Taylor's challenge on the Egyptian fell straight to the Brazilian.
An injury-time goal from Burnley substitute Gudmundsson threatened a dramatic finish, but Mane - who had earlier hit the crossbar - finished the job with a goal in the 93rd minute.
Remaining fixtures in the Premier League title race1st - Manchester City (P 30, GD 58, PTS 74)2nd - Liverpool (P30, GD 51, PTS 73)* date of fixtures may be changed because of clashes with potential cup ties or television coverage30 March v Fulham (A)17 March v Fulham (A)6 April* v Cardiff City (H)31 March v Tottenham (H)14 April* v Crystal Palace (A)5 April v Southampton (A)20 April v Tottenham (H)14 April v Chelsea (H)24 April v Manchester United (A)21 April v Cardiff City (A)28 April* v Burnley (A)26 April v Huddersfield Town (H)4 May* v Leicester City (H)4 May* v Newcastle United (A)12 May v Brighton (A)12 May v Wolverhampton Wanderers (H)Heaton errors hurt Burnley
For Burnley, it was a third successive defeat as they were overpowered by Liverpool, who recorded 23 shots to the visitors' three, although the Clarets did manage to score from both of their attempts on target.
Their lead, coming from Westwood's left-wing corner, came in controversial circumstances as Alisson was sandwiched between Jack Cork and Tarkowski, with the latter having his arms on the shoulders of the Brazilian and holding him down as the ball sailed over his head and into the net.
Burnley have not won at Anfield since September 1974 and boss Sean Dyche was unhappy with his side's defending and "individual errors".
Two of Liverpool's goals came from Heaton mistakes, with the goalkeeper hoping to be named in Gareth Southgate's England squad on Wednesday for the European Championship qualifiers against the Czech Republic and Montenegro.
However, one positive for Dyche and Burnley's supporters came in the shape of 19-year-old left midfielder Dwight McNeil, who, according to his manager, produced an "absolutely outstanding" performance and was "running around Anfield like a kid in a sweet shop". The Clarets' fans even had brief hope of a shock and undeserved point when Gudmundsson scored after being set up by Matej Vydra.
Burnley, in their third successive season in the top flight, are 16th in the table, only three points ahead of 18th-placed Cardiff City and face a four-game spell that is likely to be crucial to their hopes of staying in the Premier League.
They play Leicester and Wolves at home, before games against Bournemouth and Cardiff City, and Dyche will be looking for a good points haul - especially as their final four fixtures see them playing Chelsea, Manchester City, Everton and Arsenal.
Man of the match - Sadio Mane (Liverpool)Liverpool's Roberto Firmino and Adam Lallana both had excellent games, but Sadio Mane just gets the nod with two well-taken goals'We gave them three goals' - what they said
Liverpool boss Jurgen Klopp, speaking to Match of the Day, said: "Are we allowed to talk about the conditions?
"We played our game. The first Burnley goal was maybe a little bit of the wind. In most countries it would not be allowed that goal - you cannot treat the goalie like that in the six-yard box.
"Adam Lallana didn't score but he was best man on pitch. He had an outstanding game.
"At 3-1 up all the balls Burnley got were from us. I'm completely happy with the performance - especially against Burnley.
"Nobody gets rid of us."
Nobody gets rid of Liverpool - Jurgen Klopp
Burnley boss Sean Dyche, speaking to Match of the Day, said: "It was tricky. The wind was swirling. We wanted to ask questions and get the ball forward which I thought we did in spells.
"You cannot give a team like Liverpool four goals - we certainly gave them three. You can question the errors but we certainly made a game of it.
"In the first half I don't think they had too many golden chances yet we were 2-1 down. Even at 3-1, the mentality of the group was good and we got a goal back.
"If you had said to me that we would have 30 points after this stage of the season I would certainly have take it."
On McNeil's performance: "He was absolutely outstanding. He's been a big factor in our turnaround this season."
Liverpool 4-2 Burnley: Clarets mentality really pleasing - Sean DycheLiverpool extend unbeaten Anfield run - the stats
Liverpool's tally of 73 points from their opening 30 league games this season is their joint-best total at this stage of a league campaign (adjusting for three points for a win), level with the 1904-05 second tier season and 1987-88 in the top flight.The Reds are the first side to win four consecutive home Premier League games in which they conceded the first goal since Chelsea won six in a row between April 2013 and May 2015.Burnley have dropped more points from winning positions in their 30 Premier League games this season (10) than they did in the whole of 2017-18 (nine).Liverpool have now gone 36 Premier League games without a loss at Anfield (won 26, drew 10), the joint-third-longest unbeaten home run in the competition's history, behind only Chelsea (86 games between March 2004-October 2008) and Manchester City (37 between December 2010-December 2012).Liverpool have conceded nine goals in their 10 league matches in 2019, one more than they had in their 20 league games this season before the turn of the year.Roberto Firmino has now scored 10 or more league goals in all four of his seasons at Liverpool, the best 100% record of reaching double figures of any player for the club in the competition.Firmino has been directly involved in 100 goals in 175 appearances for Liverpool under Jurgen Klopp (63 goals, 37 assists), more than any other player in that time.Sadio Mane has become the fifth Liverpool player to score in six consecutive home appearances in the Premier League, after Michael Owen, Fernando Torres, Luis Suarez and Mohamed Salah.Mane has now scored 50 goals in 109 appearances for the club.Ashley Westwood scored his first Premier League goal for Burnley, and his first in any competition since April 2016 - 1,051 days ago - when he scored twice for Aston Villa against Southampton.Mohamed Salah's failure to score means Alan Shearer keeps his record of being the fastest player in Premier League history to score 50 goals for one club. Shearer scored 50 times in his first 66 games for Blackburn, while Salah has 49 in 66 for Liverpool.What's next?
Liverpool are in Champions League action on Wednesday (20:00 GMT) when they travel to Bayern Munich for the second leg of their last-16 tie after a goalless draw in the first match at Anfield.
Klopp's side then play in the Premier League on Sunday, 17 March (14:15) when they face struggling Fulham at Craven Cottage.
Burnley's next match is at home to Leicester in the league on Saturday (15:00).
